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Testimonials

Beautiful design and highest quality materials. I'm THRILLED. And as always the customer service from Libeling CANNOT be beat. I am a loyal customer and very rarely get shoes anywhere else anymore.
Their work is absolutely some of the best out there
in materials, construction, design, and comfort. I can't recommend them highly enough. I have friends who have shopped with them since hearing my praise and they all like their work as well.

I can barely walk in these shoes - because someone stops to compliment me on them and ask where I got them every five feet. I cannot go anywhere without other women going crazy for these shoes.
They fit like a dream and they make every outfit special.
Well worth the price!

Thank you so very much! The first time I ordered shoes online, but very good advice from the team.
The shipment arrived in no time and the shoes are stunning!
Can't thank you enough!

Beautiful design and highest quality materials. I'm THRILLED. And as always the customer service from Libeling CANNOT be beat. I am a loyal customer and very rarely get shoes anywhere else anymore.
Their work is absolutely some of the best out there
in materials, construction, design, and comfort. I can't recommend them highly enough. I have friends who have shopped with them since hearing my praise and they all like their work as well.

I can barely walk in these shoes - because someone stops to compliment me on them and ask where I got them every five feet. I cannot go anywhere without other women going crazy for these shoes.
They fit like a dream and they make every outfit special.
Well worth the price!

To change the stacking order, try adding the following declaration to your
p:nth-of-type(1)
rule:

You should now see the finished example, with the green paragraph on top:

Note that
z-index
only accepts unitless index values; you can't specify that you want one element to be 23 pixels up the Z-axis — it doesn't work like that. Higher values will go above lower values, and it is up to you what values you use. Using 2 and 3 would give the same effect as 300 and 40000.

Let's now look at fixed positioning. This works in exactly the same way as absolutepositioning, with one key difference: whereas absolute positioning fixes an element in place relative to the
<html>
element or its nearest positioned ancestor, fixed positioning fixes an element in place relative to the browser viewport itself. This means that you can create useful UI items that are fixed in place, like persisting navigation menus.

Let's put together a simple example to show what we mean. First of all, delete the existing
p:nth-of-type(1)
and
.positioned
rules from your CSS.

Now, update the
body
rule to remove the
position: relative;
declaration and add a fixed height, like so:

Now we're going to give the element
position: fixed;
, and get it to sit at the top center of the viewport. Add the following rule to your CSS:

The
top: 0;
is required to make it stick to the top of the screen; we then give the heading the same width as the content column and use the faithful old
margin: 0 auto;
trick to center it. We then give it a white background and some padding, so the content won't be visible underneath it.

If you save and refresh now, you'll see a fun little effect whereby the heading stays fixed, and the content appears to scroll up and disappear underneath it. But we could improve this more — at the moment some of the content starts off underneath the heading. This is because the positioned heading no longer appears in the document flow, so the rest of the content moves up to the top. We need to move it all down a bit; we can do this by setting some top margin on the first paragraph. Add this now:

You should now see the finished example:

Although this product differs from the tensor product, the kernel of
Alt
is precisely the ideal
I
(again, assuming that
K
has characteristic 0), and there is a canonical isomorphism

The exterior product of two alternating tensors
t
and
s
of ranks
r
and
p
is given by

The components of this tensor are precisely the skew part of the components of the tensor product
s
⊗
t
, denoted by square brackets on the indices:

The interior product may also be described in index notation as follows. Let
t
=
t
i
0
i
1
⋯
i
r
−
1
{\displaystyle t=t^{i_{0}i_{1}\cdots i_{r-1}}}
be an antisymmetric tensor of rank
r
. Then, for
α
∈
V
∗
,
i
α
t
is an alternating tensor of rank
r
− 1
, given by